The Enzyme-Substrate Complex

AH reactions catalyzed by enzymes are in theory reversible. However, in practice the reaction is usually found to be more rapid in one direction than in the other, so that an equilibrium is reached in which the product of either the forward or the backward reaction predominates, sometimes so markedly that the reaction is virtually irreversible. 

If the product of the reaction in one direction is removed as it is formed (e.g., because it is the substrate of a second enzyme present in the reaction mixture), the equilibrium of the first enzymatic process will be displaced so that the reaction will proceed to completion in that direction. Reaction sequences in which the product of one enzyme-catalyzed reaction becomes the substrate of the next enzyme and so on, often through many stages, are characteristic of biologi- 

When a secondary enzyme-catalyzed reaction, known as an indicator reaction, is used to determine the activity of a different enzyme, the primary reaction catalyzed by the enzyme to be determined must be the rate-limiting step. Conditions are chosen to ensure that the rate of reaction catalyzed by the indicator enzyme is directly proportional to the rate of product formation in the first reaction. 

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Michaelis constant An experimentally determined parameter inversely indicative of the affinity of an enzyme for its substrate. For a constant enzyme concentration, the Michaelis constant is that substrate concentration at which the rate of reaction is half its maximum rate. In general, the Michaelis constant is equivalent to the dissociation constant of the enzyme-substrate complex. 

To be analytically useful equation 13.16 needs to be written in terms of the concentrations of enzyme and substrate. This is accomplished by applying the steady-state approximation, in which we assume that the concentration of ES is essentially constant. After an initial period in which the enzyme-substrate complex first forms, the rate of formation of ES... 

Like a noncompetitive inhibitor, an uncompetitive inhibitor does not compete with the substrate since it binds to the enzyme—substrate complex but not to the free enzyme. Uncompetitive inhibition... 

The concentration of the enzyme-substrate complex from Equation 11-3 is... 

The three most common types of inhibitors in enzymatic reactions are competitive, non-competitive, and uncompetitive. Competitive inliibition occurs when tlie substrate and inhibitor have similar molecules that compete for the identical site on the enzyme. Non-competitive inhibition results in enzymes containing at least two different types of sites. The inhibitor attaches to only one type of site and the substrate only to the other. Uncompetitive inhibition occurs when the inhibitor deactivates the enzyme substrate complex. The effect of an inhibitor is determined by measuring the enzyme velocity at various... 

The Michaelis constant has the units of a dissociation constant however, the dissociation constant of the enzyme—substrate complex is k dk, which is not equal to Km unless k 2-... 

The interpretations of Michaelis and Menten were refined and extended in 1925 by Briggs and Haldane, by assuming the concentration of the enzyme-substrate complex ES quickly reaches a constant value in such a dynamic system. That is, ES is formed as rapidly from E + S as it disappears by its two possible fates dissociation to regenerate E + S, and reaction to form E + P. This assumption is termed the steady-state assumption and is expressed as... 

There are important consequences for this statement. The enzyme must stabilize the transition-state complex, EX, more than it stabilizes the substrate complex, ES. Put another way, enzymes are designed by nature to bind the transition-state structure more tightly than the substrate (or the product). The dissociation constant for the enzyme-substrate complex is... 

When the enzyme-substrate complex is stabilised, it may reach a fixed concentration, therefore there is no more change in ES ... 

The enzyme-substrate complex is used by substituting ES into (5.7.1.23) ... 

The affinity of an enzyme for its substrate is the inverse of the dissociation constant for dissociation of the enzyme substrate complex ES. 

Inhibitors can bind directly to the free form of the enzyme, to an enzyme species that follows formation of the enzyme-substrate complex, or to both. 

An inhibitor that binds exclusively to the free enzyme (i.e., for which a = °°) is said to be competitive because the binding of the inhibitor and the substrate to the enzyme are mutually exclusive hence these inhibitors compete with the substrate for the pool of free enzyme molecules. Referring back to the relationships between the steady state kinetic constants and the steps in catalysis (Figure 2.8), one would expect inhibitors that conform to this mechanism to affect the apparent value of KM (which relates to formation of the enzyme-substrate complex) and VmJKM, but not the value of Vmax (which relates to the chemical steps subsequent to ES complex formation). The presence of a competitive inhibitor thus influences the steady state velocity equation as described by Equation (3.1) ... 

A noncompetitive inhibitor is one that displays binding affinity for both the free enzyme and the enzyme-substrate complex or subsequent species. In this situation the binding affinity cannot be defined by a single equilibrium dissociation constant ... 

The first step in an enzymatic reaction is the relatively rapid formation of the enzyme-substrate complex (ES) [57],... 

Ethanolamine ammonia lyase has a molecular weight of 520,000 and consists of 8 or 10 subunits. Two 5 -deoxyadenosylcobalamin molecular bind per enzyme molecule, and recent kinetic studies by Babior show that these two molecules carry out catalysis independently. Evidence is available that this enzyme functions by a radical mechanism since both spin labeling and Co(II) esr experiments indicate that Co(II) is an intermediate during H-transfer. Also, 5 -deoxyadenosine has been detected as a product of oxygenation of the enzyme-substrate complex (99—101). 

In an unpublished study, Grieger and Hansel have used absorbance measurements to monitor the progress of the reaction forming an enzyme-substrate complex of imidazole (S) and metmyo-globin (E) at high pressures. Formation of the enzyme-substrate complex (ES) may be represented by the following equation... 

E represents the enzyme S represents the substrate ES represents the enzyme-substrate complex P represents the product of the reaction... 

Although the Michaelis-Menten equation is applicable to a wide variety of enzyme catalyzed reactions, it is not appropriate for reversible reactions and multiple-substrate reactions. However, the generalized steady-state analysis remains applicable. Consider the case of reversible decomposition of the enzyme-substrate complex into a product molecule and enzyme with mechanistic equations. 

Later on12, Koshland proposed the induced fit model of the active site action that considers that during the formation of the enzyme-substrate complex, the enzyme can change its conformation so as to wrap the substrate like it happens when a hand (substrate) fits in a globe (enzyme). This flexing puts the active site and bonds in the substrate under strain, which weakens the bonds and helps to lower the activation energy for the catalyzed reaction. 

Micromoles of product made per minute per micromole of enzyme (VmJEt). The kcat is the first-order rate constant for the conversion of the enzyme-substrate complex to product. 

The turnover number, or kCM (pronounced kay kat ), is another way of expressing Vmax. It s Vmax divided by the total concentration of enzyme (Vmax/E,). The kcat is a specific activity in which the amount of enzyme is expressed in micromoles rather than milligrams. The actual units of kcat are micromoles of product per minute per micromole of enzyme. Frequently, the micromoles cancel (even though they re not exactly the same), to give you units of reciprocal minutes (min-1). Notice that this has the same units as a first-order rate constant (see later, or see Chap. 24). The kcat is the first-order rate constant for conversion of the enzyme-substrate complex to product. For a very simple mechanism, such as the one shown earlier, kcat would be equal to k3. For more complex... 

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